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Bulletin of the London Mathematical Society Advance Access originally published online on April 7, 2009
Bulletin of the London Mathematical Society 2009 41(3):515-523; doi:10.1112/blms/bdp023
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© 2009 London Mathematical Society

The equivariant Euler characteristic of real Coxeter toric varieties

Anthony Henderson and Gus Lehrer

School of Mathematics and Statistics
University of Sydney
NSW 2006
Australia
anthonyh@maths.usyd.edu.au

Received 4 June 2008. Revision received 30 October 2008.

Let W be a Weyl group, and let TW be the complex toric variety attached to the fan of cones corresponding to the reflecting hyperplanes of W, and its weight lattice. The real locus TW(R) is a smooth, connected, compact manifold with a W-action. We give a formula for the equivariant Euler characteristic of TW(R) as a generalised character of W. In type An–1 for n odd, one obtains a generalised character of Symn whose degree is (up to sign) the nth Euler number.

2000 Mathematics Subject Classification 14M25, 14P25 (primary), 20C30, 14L30 (secondary).


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